Both the girls had allegedly been forcibly converted to Islam and gotten married to Muslim boys.
The apex court observed that the two girls should be allowed to make a decision on whether they want to go with their parents or husbands based on free will.
The Supreme Court will again take up the matter on April 18.
A three-member bench, headed by Chief Justice Iftikhar Muhammad Chaudhry, took up the two applications calling for holding meetings with the Hindu girls at Panah, a shelter home in Karachi.
Naveed Shah, the husband of Rinkle Kumari, moved an application through his counsel Mujeeb Peerzada, with a request to allow him to meet his wife, who is staying at the shelter home in Karachi, contending that police was not permitting him to meet her.
Similarly, Dr Ramesh, the father of the other girl Dr Lata, also submitted a plea through his counsel Nasir Mengal, for meeting with his daughter at the shelter home.
During the hearing, Mujeeb Peerzada, the counsel for Naveed Shah, said that policemen were not allowing his client to meet with his wife (Rinkle Kumari) at the shelter home.
He said that his client had also not been allowed to give her clothes.
“You must be aware that she (Rinkle) wanted to go with her mother on the last date of hearing.
Let her think about her future till the next date of hearing,” the Chief Justice urged.
The court, however, asked the learned counsel to hand over clothes and other such things to the Advocate-General of Sindh, saying that he would provide her at the shelter home.
Meanwhile, Nasir Mengal, the counsel for Dr Ramesh, also requested the court to allow his client to meet with his daughter but the court declined this plea as well.
On March 26, the court had sent the two Hindu girls to the Karachi-based shelter home, urging them to make a free will decision about their future – whether they wanted to go with parents or husbands.
The CJP had observed: “Let these girls have some free time to think over and decide about their future themselves.
Now there is pressure of the court, police, their husbands and parents on them.” The atmosphere in the court was very tense on the last date of hearing, as the girls’ parents demanded that their daughters be allowed to go with them.
One of the girls, Rinkle Kumari (pictured), whose new name after conversion is Faryal Bibi, cried and begged: “I want to go with my parents.” Dr Lata Kumari, now Hifza Bibi, said: “Let me talk to my father.” Dr Lata’s father Dr Ramesh Kumar created a commotion in the courtroom when he shouted that his daughter should be allowed to go with him in accordance with her free will.